Dynamical models of tuberculosis and their applications
Dynamical models of tuberculosis and their applications
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DOI：
10.3934/mbe.2004.1.361
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发表时间：
2004-09-01
影响因子：
2.6
通讯作者：
Song, BJ
中科院分区：
文献类型：
--
作者：
Castillo-Chavez, C;Song, BJ
20世纪80年代至90年代初，结核病（TB）的重新出现促使人们对结核病流行病传播动力学背后的机制进行了广泛的研究。本文对结核病的动态和控制方面的工作进行了详细的回顾。描述结核病动态的最早的数学模型出现在20世纪60年代，并侧重于使用模拟方法的预测和控制策略。最近开发的模型不仅注意模拟，而且还考虑使用现代知识的动态系统的动态分析。这些模型所解决的问题主要集中在结核病控制策略、最佳疫苗接种政策、在美国消除结核病的方法，结核病与艾滋病毒/艾滋病合并感染、耐药结核病、免疫系统的反应、人口统计学的影响、公共交通系统的作用以及接触模式的影响。模型公式涉及各种数学领域，如常微分方程（自治和非自治系统），偏微分方程（偏微分方程），差分方程系统，积分微分方程系统，马尔可夫链模型和仿真模型。
The reemergence of tuberculosis (TB) from the 1980s to the early 1990s instigated extensive researches on the mechanisms behind the transmission dynamics of TB epidemics. This article provides a detailed review of the work on the dynamics and control of TB. The earliest mathematical models describing the TB dynamics appeared in the 1960s and focused on the prediction and control strategies using simulation approaches. Most recently developed models not only pay attention to simulations but also take care of dynamical analysis using modern knowledge of dynamical systems. Questions addressed by these models mainly concentrate on TB control strategies, optimal vaccination policies, approaches toward the elimination of TB in the U.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responses of the immune system, impacts of demography, the role of public transportation systems, and the impact of contact patterns. Model formulations involve a variety of mathematical areas, such as ODEs (Ordinary Differential Equations) (both autonomous and non-autonomous systems), PDEs (Partial Differential Equations), system of difference equations, system of integro-differential equations, Markov chain model, and simulation models.